2024/04/08 by Cong, Wenyu, Shi, Jingtao
#49K45 #49N70 #60H10 #91A23 #93E20 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2404.05166
This paper is concerned with an indefinite linear-quadratic mean field games of stochastic large-population system, where the individual diffusion coefficients can depend on both the state and the control of the agents. Moreover, the control weights in the cost functionals could be indefinite. A direct approach is used to derive the ε-Nash equilibrium strategy. First, we formally solving an N-player game problem within a vast and finite population setting. Subsequently, decoupling or reducing high-dimensional systems by introducing two Riccati equations explicitly yields centralized strategies, contingent on the state of a specific player and the average state of the population. As the population size N goes infinity, the construction of decentralized strategies becomes feasible. Then, we demonstrated they are an ε-Nash equilibrium. Numerical examples are provided to demonstrate the effectiveness of the proposed strategies.